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Complexity analysis of trust-region methods under -smoothness
Youssef Diouane, Mohamed L. Habiboullah, Awa Khouna +1
Generalized smoothness assumptions have attracted growing attention in recent years, motivated in part by machine learning problems in which the gradient of the objective function…
Envelopt: Constrained Convex Composite Optimization
Alberto De Marchi, Dominique Orban
We introduce Envelopt, a globally convergent iterative framework for a broad class of structured optimization problems where a smooth objective is augmented by a nonsmooth convex r…
An Inexact Modified Quasi-Newton Method for Nonsmooth Regularized Optimization
Nathan Allaire, Sébastien Le Digabel, Dominique Orban
We introduce iR2N, a modified proximal quasi-Newton method for minimizing the sum of a smooth function and a lower semi-continuous prox-bounded function , allowing inexact e…
Nonsmooth exact penalty methods for equality-constrained optimization: complexity and implementation
Youssef Diouane, Maxence Gollier, Dominique Orban
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems i…
A Proximal Modified Quasi-Newton Method for Nonsmooth Regularized Optimization
Youssef Diouane, Mohamed Laghdaf Habiboullah, Dominique Orban
We develop R2N, a modified quasi-Newton method for minimizing the sum of a function and a lower semi-continuous prox-bounded . Both and may be noncon…
Complexity of trust-region methods in the presence of unbounded Hessian approximations
Youssef Diouane, Mohamed Laghdaf Habiboullah, Dominique Orban
We extend traditional complexity analyses of trust-region methods for unconstrained, possibly nonconvex, optimization. Whereas most complexity analyses assume uniform boundedness o…
An interior-point trust-region method for nonsmooth regularized bound-constrained optimization
Geoffroy Leconte, Dominique Orban
We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence of unconstrained nonsmo…
Complexity of trust-region methods with unbounded Hessian approximations for smooth and nonsmooth optimization
Geoffroy Leconte, Dominique Orban
We develop a worst-case evaluation complexity bound for trust-region methods in the presence of unbounded Hessian approximations. We use the algorithm of arXiv:2103.15993v3 as a mo…
The Indefinite Proximal Gradient Method
Geoffroy Leconte, Dominique Orban
We introduce a variant of the proximal gradient method in which the quadratic term is diagonal but may be indefinite, and is safeguarded by a trust region. Our method is a special…